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ACADEMY OF FOR 196J

A 44.77 -- Configuration - Period in Solar-Climatic Cycles CLYDE J. BOLLINGER, Unlversltr of Oklahoma, Norman It, as appears certain, terrestrial climatic fluctuations are infiuenced by variations in the solar energy reaching the earth; and, if also, the more or less accepted theory is accepted that sun-spot activity is influenced by planetary configuration, the conclusion that climatic fluctuations are influenced by planetary configuration. is inescapable. Configuration re­ currences of Venus, Earth and Jupiter at intervals of 11.1928696 , 22.385739 years, 4~771478 years, .89.542966 years and 179,086912 years are here described. These periods are derived from the siderial and mean synodic periods of the , which are astronomic constants. The siderial (revolution) period of Earth Is 1.00004 years, Venus 0.61521 years and Jupiter 11.86223 years. If for simplification of calculations, the eccentricity of the planetary is neglected, and the three planets, Venus, Earth and Jupiter are assumed to be in to t., then at t. 44.771478 years they will again be in conjunction but in 81.25 degrees less advanced heliocentric longitude. This arises from the fact that in this period the number of revolutions of each is: Earth 44.769687 Venus 72.7743 Jupiter 3.7742884 The mean synodic period of any pair of planets may be computed from their siderial periods. Thus let z=mean synodic period of Jupiter and Venus, since the siderial period of Jupiter is 11.86223 years and that of Venus 0.61521 years we may write z z ---+1 ; whence z=0.648862 years 11.86223 .61522 The mean synodic periods of Jupiter and Earth is 1,0921098 years and of Venus and Earth, 1.598718 years. . Four Bun-spot cycle periods or 44.771878 years represents 69.0 Juplte'r­ \ enus synods, 40.9963 Jupiter-Earth synods and 28.004612 Venus-Earth synods. The number of mean synodic periods at 11.192694 year sun-spot ('\cle intervals tor the three planets are gtven In Table la. It wl1l be noted that in the cycle phase, representing sun-spot maxima, the angles, be­ ~",:een the three planets In thla phase are 90°, whereas at a hemlcycle or ~;)9643476 years removed, representing 8un-spot minima, the angular 41f- prellcee are 46°. . I TABLE I 179.08591! Year (16 P1I4ae) Jvpiter, Yen ... , Earth OOAf'I1t£rat((m OJ/cZe t.=VE/3 U!0.55° A.ug. 15, 17.f8.621!-P aAd L35.f.31! Sept. 15, 1927.70713 1 JV SJ/nod=0.648862 Years 17.25 JY 8J/nod8=11.192869.f J/ear3= -20.3144054° heliocentric Prece13((m 8.6!5 8J/Md3=5.59648475 J/ear3 (a) 90°

OBIENTATION MINIMUM MEAN SYNODIC PEBIODS CONFlGU&ATION T.=360° JUP:rrD- JUPITER- VENUS JUPITER- JUPITU- . VENUS- LoNG. YhB CTOLI: VENUS EARTH EARTH VENUS EARTH EARTH JUPITU 11.1928694 1 17.25 10.248849 7.001153 0 0 d 339.686° 23.88674 2 a4.60 20.497698 14.002306 8 8 d 319.87 ~ 38.678609 3 61.76 30.746647 21.00369 0 0 d 299.08 44.7714780 4 69.00 40.996396 28.004612 d d d 278.74 56.964349 6 86.26 51.244246 36.005765 0 0 d 266.43 67.167218 6 103.60 61.493094 42.006918 8 8 d 238.11 i 78.360087 7 120.76 71.741943 49.008071 0 0 d 217.80 .89.642966 8 138.00 81.990792 66.009224 d d d 197.49 ~ 100.735829 9 156.26 92.239641 63.010377 0 0 d 177.17 lZ 111.928698 10 172.50 102.48849 70.01153 8 8 d 168.86 0 123.121667 11 189.76 112.737339 77.012683 0 0 d 136.64 '.. 184.314436 12 207.0 122.986188 84.013836 d d d 116.23 ~ 146.607305 13 224.26 133.236037 91.014989 0 0 d 96.91 166.700174 14 241.50 143.483886 98.016142 8 8 d 76.60 ~ 187.898043 16 268.76 163.732735 .106.017295 0 0 d 66.28 0 179.086912 16 276.0 163.981584 112.018448 d d d 84.97 E i ~ •l:S ! 0 ~ TABLE 1 (Coftt.ftwed) 0 ~ (b) Phase Angle = 45 ~ SUNSPOT MAXIMUM l!J y&.U ~. 6.59643475 .6 8.626 5.124424 3.50057 8+45 0 6 +45 0 8 169.84 P.J 16.78980376 1.6 26.876 15.373273 10.5017295 0+45 0+ 45 8 149.63 27.98217276 2.6 43.125 25.622122 17.5028825 6+45 8+46 8 129.21 ~ 39.17604:176 3.6 60.375 35.870971 24.5040355 108.90 ~ 0+45 0+45 8 ... 50.36791075 4.6 77.825 46.11982 31.5051885 8+45 6+45 8 88.58 110 01.66077975 5.6 9-4.875 56.368669 38.50634'15 0+45 0+45 8 68.27 O'lto 72.75364875 6.6 112.126 66.617518 45.5074945 6+45 8+45 8 47.96 83.94861775 7.6 129.375 76.866367 52.5086475 0+45 0+ 45 8 27.64 96.13938675 8.5 148.625 87.115216 59.6098005 8+45 6+45 8 7.33 106.33225676 9.5 163.876 97.364065 66.6109535 . 0+ 45 0+45 8 347.01 117.52512476 10.5 181.125 107.612914 73.5121065 6+45 8+45 8 326.70 128.7179375 11.6 198.375 117.861763 80.6132596 0+ 45 0+45 8 306.38 139.91086275 12.6 215.625 128.110612 87.5144126 8+45 6+45 8 286.07 161.10373176 13.6 232.876 138.369461 94.5155656 0+ 45 0+ 45 8 266.76 162.29660076. 14.6 260.126 148.60831 101.5167185 6 +45 8+45 8 246." 173.48946976 16.5 267.376 158.857159 108.6178715 0+45 0+ 45 8 226.13

I PROOEEDlNGS OF "THE OKLAHOMA

Since the tlde-ralslDg force of a planet varies directly with and lnveraely as the cube of distance from the sun an expression for the com­ bined sun-tide effect of the three planets may be written: m m . m 8un-tlde 1=--,.,..J + ...-- V cos 2(LJ-LV) + --,. B cos 2(LJ-LE) Where: M=Mass, r=radiuB vector, L=heliocentric longitude and J,V and B identify the planets.

ELEVEN-YEAR JUPITER- VENUS-EARTH CYCLE f'lIttOOr IIJIZ..H ytAI" °".15 lilt... MIT£lt-I/PUS S\'NOOS.

FIGURE 1. In Figure 1. the relation between the recurrent 90° and 45° configUra­ tion patterns at 11.19269. year intervals along with smoothed monthly sun­ sPots for phase dates during the period of record starting in 17.9 are shown graphically. A consistent relation is evident except in the cycle maximum of 1782, which may, repreaent an error in the SUD-epot record. In of the above periodicities it appears probable· that the aboye formula;'when extended to include allot the planets, and perhaps f;urther ACADEMY OF SCIJDNCE FOR 1962 311 elaborated by th~ inclusion of terms for heliographic decUnatlon, wl1l enable investigators to proceed directly from astronomic data to the exploration of terra incognUo-ln the fields of climatology and meteorology a8 well as to the interpretation of cycles now recognized, but not explained, In many catagories terrestrial phenomena. Thus the slow progress which In the past, it appears, may have been due to insufficient knowledge of sunspot cycle variation and/or a dearth of rellable "solar constant" datiL may be accelerated.